Question

What will be the minimum pressure required to compress 500 dm\(^3\) of air at 1 bar to 200 dm\(^3\) at 30\(^\circ\)C?

• A. 2.5 bar
• B. 1 bar
• C. 2 bar
• D. 3 bar

Hint:

For isothermal processes, pressure and volume are inversely proportional.

Answer 1

The Correct Option is A

Step 1: Identify the gas law to be used.
Since temperature is constant, Boyle’s law applies.
\[ P_1V_1 = P_2V_2 \]
Step 2: Substitute the given values.
\[ P_1 = 1\ \text{bar}, \quad V_1 = 500\ \text{dm}^3 \]
\[ V_2 = 200\ \text{dm}^3 \]
Step 3: Calculate final pressure.
\[ P_2 = \frac{P_1V_1}{V_2} = \frac{1 \times 500}{200} \]
\[ P_2 = 2.5\ \text{bar} \]
Step 4: Conclusion.
Minimum pressure required is 2.5 bar.